Syntheses and Patterns of Changes in Structural Parameters of the New Quaternary Tellurides EuRECuTe3 (RE = Ho, Tm, and Sc): Experiment and Theory

The layered orthorhombic quaternary tellurides EuRECuTe3 (RE = Ho, Tm, Sc) with Cmcm symmetry were first synthesized. Single crystals of the compounds up to 500 μm in size were obtained by the halide-flux method at 1120 K from elements taken in a ratio of Eu/RE/Cu/Te = 1:1:1:3. In the series of compounds, the changes in lattice parameters were in the ranges a = 4.3129(3)–4.2341(3) Å, b = 14.3150(9)–14.1562(9) Å, c = 11.2312(7)–10.8698(7) Å, V = 693.40(8)–651.52(7) Å3. In the structures, the cations Eu2+, RE3+ (RE = Ho, Tm, Sc), and Cu+ occupied independent crystallographic positions. The structures were built with distorted copper tetrahedra forming infinite chains [CuTe4]7− and octahedra [RETe6]9− forming two-dimensional layers along the a-axis. These coordination polyhedra formed parallel two-dimensional layers CuRETe32−∞2. Between the layers, along the a-axis, chains of europium trigonal prisms [EuTe6]10− were located. Regularities in the variation of structural parameters and the degree of distortion of coordination polyhedra depending on the ionic radius of the rare-earth metal in the compounds EuRECuCh3 (RE = Ho, Er, Tm, Lu, Sc; Ch = S, Se, Te) were established. It is shown that with a decrease in the ionic radius ri(RE3+) in the compounds EuRECuTe3, the unit-cell volume, bond length d(RE–Te), distortion degree [CuTe4]7−, and crystallographic compression of layers [RECuTe3]2− decreased. The distortion degree of tetrahedral polyhedra [CuCh4]7−, as well as the structural parameters in europium rare-earth copper tellurides EuRECuTe3, were higher than in isostructural quaternary chalcogenides. Ab initio calculations of the crystalline structure, phonon spectrum, and elastic properties of compounds EuRECuTe3 (RE = Ho, Tm, and Sc) ere conducted. The types and wave numbers of fundamental modes were determined, and the involvement of ions in IR and Raman modes was assessed. The calculated data of the crystal structure correlated well with the experimental results.


Introduction
Studying four-component tellurides opens up new perspectives for creating materials with unique properties and potential applications in various fields, including electronics, optics, and energy [1][2][3][4][5][6].Understanding the influence of structural features on the properties of chalcogenide materials allows for the modification of the band gap width, electrical, and optical properties of the materials [7][8][9][10][11][12][13][14][15].The presence of a large variety of coordination polyhedra and different ways of connecting them in tellurides creates conditions for the formation of layered or tunnel structures [6,9].Layered tellurides of the space group Cmcm demonstrate promising efficiency in solar energy conversion and are considered as prospective absorbers in solar cell structures, as well as thermoelectric materials [1][2][3][4].It is assumed that in compounds of the space group Cmcm, such as MRECuTe 3 (M = d-element) with the structure type of KZrCuS 3 , there is a covalently bonded sublattice [RECuTe 3 ] 2− , leading to improved electrical transport properties, and the M 2+ cations induce low lattice thermal conductivity [1,2].Tellurides of the space group Cmcm contain non-centrosymmetric tetrahedral coordination polyhedra [16], allowing them to be used in nonlinear optical devices as photon media [17,18].In the EuRECuCh 3 structures, a tetrahedral structural motif is clearly visible in the form of one-dimensional chains of distorted [CuCh 3 ] 5− [18][19][20][21][22][23][24][25][26] tetrahedra.Compounds BaRECuCh 3 (Ch = chalcogen) are used as hole transport materials in solar cells, significantly increasing the efficiency of the solar cell (up to 45%) compared to a cell without this chalcogenide [1,27,28].It was previously established that replacing the alkaline earth M 2+ ions in the quaternary chalcogenides MRECuCh 3 with the Eu 2+ cation makes it possible to narrow the band gap of the compound due to the presence of the 4f-5d transition in the Eu 2+ ion [8].Also, an increase in the chalcogen radius in the series r i (S 2− ) > r i (Se 2− ) > r i (Te 2− ) reduces the value of the band gap [7].Thus, it is expected that the synthesis of EuRECuTe 3 compounds will make it possible in the future to obtain semiconductor materials with the bandgap value required for photovoltaic materials and use them as a photoanode in multilayer solar cells, improving charge separation as well as reducing the recombination of electrons and holes at the interface of the photoanode and electrolyte.

Synthesis
Single crystals of EuRECuTe3 (RE = Ho, Tm, Sc) were synthesized from elements taken in a ratio of Cu/Eu/RE/Te = 1:1:1:3 with the addition of cesium iodide as a flux.Due to the rapid oxidizability of rare-earth metals by components of the air (oxygen, carbon dioxide, water vapor) at room temperature, the starting components were weighed in an inert atmosphere using a glovebox.A layer of amorphous carbon obtained by pyrolysis of acetylene was pre-applied to the inner walls of the silica ampoules.After filling the ampoules with the starting components, they were tightly sealed with a quick-release seal, removed from the glove box, connected to a vacuum pump, evacuated to a residual pressure of 2 × 10 −3 mbar, sealed, and heated in a muffle furnace.The temperature in the furnace was raised from room temperature to 1120 K over 30 h with subsequent isothermal holding for 96 h.Cooling was carried out to 570 K over 140 h and to 300 K over 3 h.Residual flux from the sample was removed with demineralized water.The products were black needle-like crystals of EuRECuTe3 (RE = Ho, Tm, Sc) up to 500 µm in size (Figure 2).The obtained crystals were suitable for single crystal X-ray diffraction analysis.Unfortunately, it was not possible to obtain high-quality powder diffraction patterns, as copper compounds strongly absorb molybdenum radiation.The yield of tellurides was 10-15%, which did not allow for the experimental determination of the optical properties of the samples.Unfortunately, despite numerous attempts, we were unable to obtain the compound EuYbCuTe3 using the flux method.The samples after synthesis contained single crystals of Cu0.37YbTe2, EuTe, and YbTe.The phase of EuYbCuTe3 was not found in the samples, possibly due to the weak oxidizing ability of tellurium interfering with the Yb 0 -3e -→Yb 3+ redox reaction.[1,16,17,30,31], Sr [1,12,16], Eu [19,20].Description: color background corresponds to a defined structure type (space group Pnma-orange (Eu 2 CuS 3 ); space group Cmcm-green (KZrCuS 3 )).The black line delimits the regions of existence of the space groups Pnma and Cmcm.

Synthesis
Single crystals of EuRECuTe 3 (RE = Ho, Tm, Sc) were synthesized from elements taken in a ratio of Cu/Eu/RE/Te = 1:1:1:3 with the addition of cesium iodide as a flux.Due to the rapid oxidizability of rare-earth metals by components of the air (oxygen, carbon dioxide, water vapor) at room temperature, the starting components were weighed in an inert atmosphere using a glovebox.A layer of amorphous carbon obtained by pyrolysis of acetylene was pre-applied to the inner walls of the silica ampoules.After filling the ampoules with the starting components, they were tightly sealed with a quick-release seal, removed from the glove box, connected to a vacuum pump, evacuated to a residual pressure of 2 × 10 −3 mbar, sealed, and heated in a muffle furnace.The temperature in the furnace was raised from room temperature to 1120 K over 30 h with subsequent isothermal holding for 96 h.Cooling was carried out to 570 K over 140 h and to 300 K over 3 h.Residual flux from the sample was removed with demineralized water.The products were black needle-like crystals of EuRECuTe 3 (RE = Ho, Tm, Sc) up to 500 µm in size (Figure 2).The obtained crystals were suitable for single crystal X-ray diffraction analysis.Unfortunately, it was not possible to obtain high-quality powder diffraction patterns, as copper compounds strongly absorb molybdenum radiation.The yield of tellurides was 10-15%, which did not allow for the experimental determination of the optical properties of the samples.Unfortunately, despite numerous attempts, we were unable to obtain the compound EuYbCuTe 3 using the flux method.The samples after synthesis contained single crystals of Cu 0.37 YbTe 2 , EuTe, and YbTe.The phase of EuYbCuTe 3 was not found in the samples, possibly due to the weak oxidizing ability of tellurium interfering with the Yb 0 -3e − →Yb 3+ redox reaction.

X-ray Diffraction Analysis
The intensities from a single crystal of the EuRECuTe3 (RE = Ho, Tm, Sc) were collected at 293(2) K using a SMART APEX II single-crystal diffractometer (Bruker AXS, Billerica, MA, USA) equipped with a CCD-detector, graphite monochromator, and Mo-Kα radiation source.The parameters of the unit cell were determined and refined for a set of 11,880 reflections.The parameters of the unit cell correspond to the orthorhombic crystal system.The space group Cmcm was determined from the statistical analysis of all intensities.Absorption corrections were applied using the SADABS program.The crystal structure was solved by direct methods using the SHELXS program and refined in an anisotropic approximation using the SHELXL program [40].Structural investigations for the presence of missing symmetry elements were conducted using the PLATON program [41].The crystallographic data are deposited in Cambridge Crystallographic Data Centre.The data can be downloaded from the site www.ccdc.cam.ac.uk/data_request/cif (accessed on 25 February 2024).

DFT Calculations
Calculations were performed at the theoretical level DFT by using hybrid functional B3LYP [42] that take into account non-local exchange at Hartree-Fock formalism.This approach is suitable for to compounds with ionic and covalent chemical bonds.We used CRYSTAL17 code [43].The program is designed for modeling periodic compounds within the framework of the MO-LCAO approach.Stuttgart pseudopotentials ECPnMWB for Eu 2+ and RE 3+ cations were used [44].Here, n is the number of electrons that replaces this pseudopotential.For Eu 2+ , n was equal Z-10, and for RE 3+ , n was equal Z-11 (Z is atomic number).For outer shells 5s 2 5p 6 of rare-earth metal ions, which were involved in chemical bonds, attached basis sets of TZVP type were used [44].For scandium and copper, we used all-electron basis sets «Sc_pob_TZVP_2012» and «Cu_86-4111(41D)G_doll_2000», available on the website of program CRYSTAL [43].For tellurium, we used an all-electron basis set [45] also.Gaussian-type orbitals with exponents lower than 0.1 were cancelled from the basis sets.Self-consistent field was calculated with tolerance 10 -9 a.u.Monkhorst-Pack grid used was 8 × 8 × 8 k-points.
Optimization of the crystal structure was performed at first.After that, elastic constants and phonon spectrum were calculated for optimized crystal structure.

Crystal Structures of the EuRECuTe3 (RE = Ho, Tm, Sc)
In the series of europium tellurides EuRECuTe3, only three orthorhombic compounds EuRECuTe3 (RE = Gd [20], Er [19], Lu [20]) have been previously obtained using the halide flux method.The compound EuGdCuTe3 [20] crystallizes in the space group Pnma in the

X-ray Diffraction Analysis
The intensities from a single crystal of the EuRECuTe 3 (RE = Ho, Tm, Sc) were collected at 293(2) K using a SMART APEX II single-crystal diffractometer (Bruker AXS, Billerica, MA, USA) equipped with a CCD-detector, graphite monochromator, and Mo-K α radiation source.The parameters of the unit cell were determined and refined for a set of 11,880 reflections.The parameters of the unit cell correspond to the orthorhombic crystal system.The space group Cmcm was determined from the statistical analysis of all intensities.Absorption corrections were applied using the SADABS program.The crystal structure was solved by direct methods using the SHELXS program and refined in an anisotropic approximation using the SHELXL program [40].Structural investigations for the presence of missing symmetry elements were conducted using the PLATON program [41].The crystallographic data are deposited in Cambridge Crystallographic Data Centre.The data can be downloaded from the site www.ccdc.cam.ac.uk/data_request/cif (accessed on 25 February 2024).

DFT Calculations
Calculations were performed at the theoretical level DFT by using hybrid functional B3LYP [42] that take into account non-local exchange at Hartree-Fock formalism.This approach is suitable for to compounds with ionic and covalent chemical bonds.We used CRYSTAL17 code [43].The program is designed for modeling periodic compounds within the framework of the MO-LCAO approach.Stuttgart pseudopotentials ECPnMWB for Eu 2+ and RE 3+ cations were used [44].Here, n is the number of electrons that replaces this pseudopotential.For Eu 2+ , n was equal Z-10, and for RE 3+ , n was equal Z-11 (Z is atomic number).For outer shells 5s 2 5p 6 of rare-earth metal ions, which were involved in chemical bonds, attached basis sets of TZVP type were used [44].For scandium and copper, we used all-electron basis sets «Sc_pob_TZVP_2012» and «Cu_86-4111(41D)G_doll_2000», available on the website of program CRYSTAL [43].For tellurium, we used an all-electron basis set [45] also.Gaussian-type orbitals with exponents lower than 0.1 were cancelled from the basis sets.Self-consistent field was calculated with tolerance 10 −9 a.u.Monkhorst-Pack grid used was 8 × 8 × 8 k-points.
Optimization of the crystal structure was performed at first.After that, elastic constants and phonon spectrum were calculated for optimized crystal structure.

Crystal Structures of the EuRECuTe 3 (RE = Ho, Tm, Sc)
In the series of europium tellurides EuRECuTe 3 , only three orthorhombic compounds EuRECuTe 3 (RE = Gd [20], Er [19], Lu [20]) have been previously obtained using the halide flux method.The compound EuGdCuTe 3 [20] crystallizes in the space group Pnma in the structure type of Eu 2 CuS 3 , while the compounds EuErCuTe 3 [19] and EuLuCuTe 3 [20] crystallize in the space group Cmcm in the structure type of KZrCuS 3 .Single-crystal X-ray diffraction analysis revealed that the compounds EuRECuTe 3 (RE = Ho, Tm, Sc) are isostructural to EuRECuTe 3 (RE = Er [19], Lu [20]).Crystallographic data and data collection conditions are presented in Table 1.The atomic coordinates, thermal displacement parameters, bond lengths, and valence angles are presented in Tables S1-S3 of the Supplementary Material.The lattice parameters obtained from DFT calculations of EuRECuTe 3 (RE = Ho, Tm, Lu, Sc; Table S4) were in good agreement with the experimentally determined values (Table 1).The compound EuYbCuTe 3 was unable to be obtained using the halide flux method, but since Yb 3+ lies between Tm 3+ and Lu 3+ , whose quaternary tellurides crystallize in the structure type of KZrCuS 3 , if EuYbCuTe 3 is experimentally obtained by another method, it will also crystallize in this structure type.Based on this assumption, DFT calculations of the crystal structure, phonon spectrum, and elastic properties of EuYbCuTe 3 were carried out in this study.The calculated values of the electronic parameters and volume were in line with the general trend of their variations (Figures 3 and 4).
In the structures of EuRECuTe3 (RE = Ho, Tm, Sc), four distances d(Cu-Te) are shorter than the theoretical value of 2.81 Å [32] by 5-7%, while the fifth and sixth distances (4.293-4.086Å) are longer by 45-52% (Figure S1).The typical coordination polyhedron of copper in this structure is a tetrahedron (Figures 5 and S1).The tetrahedra [CuTe4] 7− are linked by shared anions (Te1) 2− along the a-axis (Figure 5).As the rare-earth metal cation radius decreased in the quaternary tellurides, a decrease in the ionicity of the Cu-Te bond was observed in the tetrahedra, resulting in the bond lengths d(Cu-Te) changing from 2.644 to 2.615 Å and from 2.668 to 2.620 Å (Table S3, Figure 6).The values of the valence angles ∠(Te-Cu-Te), ranging from 104.4 to 111.0 • (Table S3), deviate from the ideal tetrahedral angle by 1-4%.As the compound changed from EuHoCuTe 3 to EuScCuTe 3 , this deviation decreases.The reduction in the distortion of [CuTe 4 ] 7− in the series of compounds EuRECuTe 3 (RE = Ho-Lu, Sc) is confirmed by the calculation of the τ 4 descriptor [46], which increases in this series from 0.977 to 0.992 (Figure 7).Since the τ 4 descriptor values for an ideal tetrahedron, trigonal pyramid, square pyramid, and ideal square are 1.00, 0.85, 0.64-0.07,and 0.00, respectively [46], in the structures of EuRECuTe 3 , a distortion of the copper coordination polyhedron from an ideal tetrahedron to a trigonal pyramid is observed at 2.3-0.8%.The scandium telluride possesses an almost ideal tetrahedral coordination environment.The degree of distortion of the tetrahedral [CuCh 4 ] 7− polyhedra (Ch = Se, Te) in the tellurides EuRECuTe 3 was found to be higher than in the selenides EuRECuSe 3 (Figure 7).pyramid, and ideal square are 1.00, 0.85, 0.64-0.07,and 0.00, respectively [46], in the structures of EuRECuTe3, a distortion of the copper coordination polyhedron from an ideal tetrahedron to a trigonal pyramid is observed at 2.3-0.8%.The scandium telluride possesses an almost ideal tetrahedral coordination environment.The degree of distortion of the tetrahedral [CuCh4] 7-polyhedra (Ch = Se, Te) in the tellurides EuRECuTe3 was found to be higher than in the selenides EuRECuSe3 (Figure 7).Lu [20], Sc [this work]) and EuRECuSe3 (RE = Er [26], Tm-Lu [25], Sc [18]) in the space group Cmcm.
The crystal structure of compounds EuRECuTe 3 (RE = Ho-Lu, Sc) is formed by parallel two-dimensional layers in the ac-plane, consisting of octahedra and tetrahedra, which are separated by one-dimensional chains of trigonal prisms (Figure 5).
tion to states near the top of the VB.Orbitals of RE 3+ (Sc 3+ ) and europium provide the main contribution to the bottom of the CB.Calculations predicted for EuRECuTe3 (RE = Ho, Tm, Yb, Lu) the indirect band gap Г-Y.The value of the band gap (1.7-1.8 eV) was a HOMO-LUMO estimation (Table 2).This value is close to experimental data for selenides (Eu-ErCuSe3 1.79 eV [26]).For EuScCuTe3, the calculation predicted a smaller gap, equal to 1.2 eV.

Elastic Constants and Elastic Modulus
The elastic constants and elastic modulus of the compound EuRECuTe3 (RE = Ho, Tm, Yb, Lu, Sc) are presented in Table 3.The table presents the bulk module (B), shear module (G), Young's module (Y), and Poisson ratio.These are values for a polycrystal and were calculated by averaging the schemes of Voigt, Reuss, and Hill.The Voigt scheme assumes the uniformity of local strains.The Reuss scheme assumes the uniformity of local stresses.

Elastic Constants and Elastic Modulus
The elastic constants and elastic modulus of the compound EuRECuTe 3 (RE = Ho, Tm, Yb, Lu, Sc) are presented in Table 3.The table presents the bulk module (B), shear module (G), Young's module (Y), and Poisson ratio.These are values for a polycrystal and were calculated by averaging the schemes of Voigt, Reuss, and Hill.The Voigt scheme assumes the uniformity of local strains.The Reuss scheme assumes the uniformity of local stresses.The Voigt scheme provides the upper bound, whereas the Reuss scheme provides the lower bound of value.The approximation of Hill is the average of Voigt and Reuss estimations [47].The Voigt and Reuss estimates were found to be very different (Table 3), which indicates anisotropy of the elastic properties.The dependence of Young's modulus on direction also illustrates the strong anisotropy of elastic properties (Figure 10).We also calculated the universal elastic anisotropy index (1).The closer to zero this index is, the lower the anisotropy of elastic properties [48].By the lanthanoid pressure, at the row EuRECuTe 3 (RE = Ho-Lu), anisotropy decreases (Table 3).
The empirical Formula (2) was used to calculate hardness.According to [49], the formula is based on correlations between Vickers hardness (H V ) and the ratio of shear and bulk moduli.The parameters of the formula were determined from reproducing the hardness of more than forty compounds with ionic and covalent bonds [49].The shear (G) and bulk (B) modulus in ( 2) is according to the Hill estimate.

Raman, IR, and Phonon Spectra
From the DFT calculation, the wavenumbers and types of modes were determined (Tables 4 and 5).The displacement vectors were obtained from the calculations also.This made it possible to evaluate the participation of each ion in a particular mode.The values of ion displacements characterized their participation in the mode (Figures 11 and 12).According to calculations, the phonon spectrum of the crystals EuRECuTe3 (RE = Ho, Tm, Yb, Lu) at the gamma point lay in the frequency range up to 160 cm -1 (Table 4, Figure 11).In this frequency range, not only were light copper ions involved, but also telluride anions and RE 3+ cations (Figures 11 and 12).The phonon spectrum of the crystals EuScCuTe3 at

Raman, IR, and Phonon Spectra
From the DFT calculation, the wavenumbers and types of modes were determined (Tables 4 and 5).The displacement vectors were obtained from the calculations also.This made it possible to evaluate the participation of each ion in a particular mode.The values of ion displacements characterized their participation in the mode (Figures 11 and 12).According to calculations, the phonon spectrum of the crystals EuRECuTe 3 (RE = Ho, Tm, Yb, Lu) at the gamma point lay in the frequency range up to 160 cm −1 (Table 4, Figure 11).In this frequency range, not only were light copper ions involved, but also telluride anions and RE 3+ cations (Figures 11 and 12).The phonon spectrum of the crystals EuScCuTe 3 at the gamma point lay in the frequency range up to 230 cm −1 (Figure 12, Table 5).This corresponded to the fact that the mass of scandium is less than that of the other RE 3+ cations.IR, Raman, and «silent» modes for all crystals are presented in Tables S6-S8.
A strong mixing of vibrations of structural units in crystals EuRECuTe 3 can be noted.In all compounds, the europium ions participated in the frequency range up to ≈95 cm −1 .Calculations predicted a gap in the phonon spectrum in the region ≈ 92-110 cm −1 for EuRECuTe 3 (Figure 11).Note that a similar gap was practically absent in the crystal EuScCuTe 3 (Figure 12).
Calculations predicted that in crystals EuRECuTe 3 (RE = Ho, Tm, Yb, Lu), the most intense Raman mode has a frequency of about 146 cm −1 (A 1g ), and the most intense infrared mode has a frequency of about 123 cm −1 (B 2u ).At the crystal EuScCuTe 3 , the most intense Raman mode has a frequency of about 172 cm −1 (B 2g ), and the most intense infrared modes has a frequency of about 125 cm −1 (B 2u ).These modes are illustrated in Figures 13 and 14.The calculated Raman spectrum for all crystals is shown in Figure 15.The results of calculating the phonon spectrum can be useful for interpreting IR and Raman spectra of rare-earth metal tellurides EuRECuTe 3 .The IR and Raman spectra of EuRECuTe 3 (RE = Ho, Tm, Lu) obtained from calculations are similar to the spectra of EuErCuTe 3 [19].It can be assumed that the experimental spectra of EuRECuTe 3 (RE = Ho, Tm, Lu) will be similar to the previously presented experimental spectrum of EuErCuTe 3 [19].the gamma point lay in the frequency range up to 230 cm −1 (Figure 12, Table 5).This corresponded to the fact that the mass of scandium is less than that of the other RE 3+ cations.IR, Raman, and «silent» modes for all crystals are presented in Tables S6-S8.
A strong mixing of vibrations of structural units in crystals EuRECuTe3 can be noted.In all compounds, the europium ions participated in the frequency range up to ≈95 cm −1 .Calculations predicted a gap in the phonon spectrum in the region ≈ 92-110 cm −1 for EuRE-CuTe3 (Figure 11).Note that a similar gap was practically absent in the crystal EuScCuTe3 (Figure 12).
Calculations predicted that in crystals EuRECuTe3 (RE = Ho, Tm, Yb, Lu), the most intense Raman mode has a frequency of about 146 cm −1 (A1g), and the most intense infrared mode has a frequency of about 123 cm −1 (B2u).At the crystal EuScCuTe3, the most intense Raman mode has a frequency of about 172 cm −1 (B2g), and the most intense infrared modes has a frequency of about 125 cm −1 (B2u).These modes are illustrated in Figures 13 and 14.The calculated Raman spectrum for all crystals is shown in Figure 15.The results of calculating the phonon spectrum can be useful for interpreting IR and Raman spectra of rareearth metal tellurides EuRECuTe3.The IR and Raman spectra of EuRECuTe3 (RE = Ho, Tm, Lu) obtained from calculations are similar to the spectra of EuErCuTe3 [19].It can be assumed that the experimental spectra of EuRECuTe3 (RE = Ho, Tm, Lu) will be similar to the previously presented experimental spectrum of EuErCuTe3 [19].    1 Superscripts "S" and "W" denote strong and weak ion displacements in the mode, respectively.
The largest ion displacement is 0.05 Å (Sc).In the case when the displacement was greater than or equal to 0.02 Å, the displacement is indicated by "S".If the displacement did not exceed 0.01 Å, then the displacement is indicated by "W".If the value of displacement was less than 0.005 Å, then the ion is not mentioned in the column "participants".The largest ion displacement was 0.040 Å (Cu).In the case when the displacement was greater than or equal to 0.02 Å, the displacement is indicated by "S".If the displacement did not exceed 0.01 Å, then the displacement is indicated by "W".If the value of displacement was less than 0.005 Å, then the ion is not mentioned in the column "participants".
The largest ion displacement is 0.05 Å (Sc).In the case when the displacement was greater than or equal to 0.02 Å, the displacement is indicated by "S".If the displacement did not exceed 0.01 Å, then the displacement is indicated by "W".If the value of displacement was less than 0.005 Å, then the ion is not mentioned in the column "participants".

Conclusions
Single crystals of layered heterometallic tellurides EuRECuTe3 (RE = Ho, Tm, and Sc) were synthesized for the first time.The orthorhombic compounds crystallized in the space group Cmcm.With a decrease in the parameters and volume of the unit cell, the bond length d(RE-Te) occurred as the ionic radius of the rare-earth metal cation decreases (RE 3+ = Ho 3+ , Er 3+ , Tm 3+ , Yb 3+ , Lu 3+ , Sc 3+ ), leading to a crystal-chemical compression of the twodimensional layers in the crystal structures of the EuRECuTe3 compounds.The patterns of changes in structural parameters were compared with the isostructural chalcogenides EuRECuCh3 (Ch = S, Se, Te) in the space group Cmcm.In the series of chalcogenides, the degree of distortion of the copper coordination polyhedra was found to be highest in the tellurides.Within the framework of the DFT approach, by using the hybrid functional, which takes into account non-local HF exchange, the crystal structure and IR, Raman, and "silent" modes were studied.Elastic tensor as well as elastic moduli and hardness were calculated.The theoretical calculations allow for the assignment of vibrational modes as

Conclusions
Single crystals of layered heterometallic tellurides EuRECuTe 3 (RE = Ho, Tm, and Sc) were synthesized for the first time.The orthorhombic compounds crystallized in the space group Cmcm.With a decrease in the parameters and volume of the unit cell, the bond length d(RE-Te) occurred as the ionic radius of the rare-earth metal cation decreases (RE 3+ = Ho 3+ , Er 3+ , Tm 3+ , Yb 3+ , Lu 3+ , Sc 3+ ), leading to a crystal-chemical compression of the two-dimensional layers in the crystal structures of the EuRECuTe 3 compounds.The patterns of changes in structural parameters were compared with the isostructural chalcogenides EuRECuCh 3 (Ch = S, Se, Te) in the space group Cmcm.In the series of chalcogenides, the degree of distortion of the copper coordination polyhedra was found to be highest in the tellurides.Within the framework of the DFT approach, by using the hybrid functional, which takes into account non-local HF exchange, the crystal structure and IR, Raman, and "silent" modes were studied.Elastic tensor as well as elastic moduli and hardness were calculated.The theoretical calculations allow for the assignment of vibrational modes as well as revealing the involved ions that participated in these modes.

Figure 2 .
Figure 2. Photograph of EuHoCuTe3 (left) and EuScCuTe3 (right) crystals placed in a capillary for X-ray diffraction analysis.

Figure 2 .
Figure 2. Photograph of EuHoCuTe 3 (left) and EuScCuTe 3 (right) crystals placed in a capillary for X-ray diffraction analysis.

Figure 4 .
Figure 4. Relationship between the unit-cell parameters (a: black, b: blue, c: red) and the ionic radius of the rare-earth metal cation in the series of compounds EuRECuTe3 (RE = Ho [this work], Er [19],

Figure 4 .
Figure 4. Relationship between the unit-cell parameters (a: black, b: blue, c: red) and the ionic radius of the rare-earth metal cation in the series of compounds EuRECuTe3 (RE = Ho [this work], Er [19],

Figure 5 .
Figure 5. Projection of the crystal structure of the EuRECuTe3 representatives in the space group Cmcm.

Figure 5 .
Figure 5. Projection of the crystal structure of the EuRECuTe 3 representatives in the space group Cmcm.

Figure 11 .
Figure 11.The values of ion displacements at phonon modes in EuYbCuTe3 (space group: Cmcm).

Figure 12 .
Figure 12.The values of ion displacements at phonon modes in EuScCuTe3 (space group: Cmcm).

Figure 13 .
Figure 13.Ion displacements in IR and Raman modes with maximum intensity at EuYbCuTe3.

Figure 13 .
Figure 13.Ion displacements in IR and Raman modes with maximum intensity at EuYbCuTe 3 .

Figure 13 .
Figure 13.Ion displacements in IR and Raman modes with maximum intensity at EuYbCuTe3.

Figure 14 .
Figure 14.Ion displacements in IR and Raman modes with maximum intensity at EuScCuTe3.

Figure 15 .
Figure 15.The simulated Raman spectra.The calculation was carried out for the exciting laser wavelength λ = 532 nm and T = 300 K.When modelling the Raman spectra based on the calculated wavenumbers and intensities, the functions pseudo-Voigt with dumping factor 8 cm −1 were used.

Table 1 .
Main parameters of processing and refinement of the EuRECuTe 3 (RE = Ho, Tm, Sc) samples.

Table 2 .
Calculated band gaps of the tellurides EuRECuTe3 (RE = Ho-Lu and Sc) in eV.

Table 2 .
Calculated band gaps of the tellurides EuRECuTe 3 (RE = Ho-Lu and Sc) in eV.

Table 3 .
Calculated elastic constants and modulus, as well as Vickers hardness (GPa) of the EuRECuTe 3 series (RE = Ho, Tm, Yb, Lu, and Sc).

Table 4 .
Phonons at the gamma point of EuYbCuTe 3 .

Table 5 .
Phonons at the gamma point of EuScCuTe 3 .
1 Superscripts "S" and "W" denote strong and weak ion displacements in the mode, respectively.

Table 4 .
Phonons at the gamma point of EuYbCuTe3.